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Fractal to Euclidean crossover and scaling for random walks on percolation clusters. II. Three‐dimensional lattices

dc.contributor.authorArgyrakis, Panosen_US
dc.contributor.authorKopelman, Raoulen_US
dc.date.accessioned2010-05-06T21:43:01Z
dc.date.available2010-05-06T21:43:01Z
dc.date.issued1985-09-15en_US
dc.identifier.citationArgyrakis, Panos; Kopelman, Raoul (1985). "Fractal to Euclidean crossover and scaling for random walks on percolation clusters. II. Three‐dimensional lattices." The Journal of Chemical Physics 83(6): 3099-3102. <http://hdl.handle.net/2027.42/70154>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/70154
dc.description.abstractWe perform random walk simulations on binary three‐dimensional simple cubic lattices covering the entire ratio of open/closed sites (fraction p) from the critical percolation threshold to the perfect crystal. We observe fractal behavior at the critical point and derive the value of the number‐of‐sites‐visited exponent, in excellent agreement with previous work or conjectures, but with a new and improved computational algorithm that extends the calculation to the long time limit. We show the crossover to the classical Euclidean behavior in these lattices and discuss its onset as a function of the fraction p. We compare the observed trends with the two‐dimensional case.en_US
dc.format.extent3102 bytes
dc.format.extent264988 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleFractal to Euclidean crossover and scaling for random walks on percolation clusters. II. Three‐dimensional latticesen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumDepartment of Chemistry, University of Michigan, Ann Arbor, Michigan, 48109‐1055en_US
dc.contributor.affiliationotherDepartment of Physics, University of Crete, Iraklion, Crete, Greeceen_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/70154/2/JCPSA6-83-6-3099-1.pdf
dc.identifier.doi10.1063/1.449215en_US
dc.identifier.sourceThe Journal of Chemical Physicsen_US
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dc.identifier.citedreferenceY. Gefen, A. Aharony, and S. Alexander, Phys. Rev. Lett. 50, 77 (1983); P. G. de Gennes, C. R. Acad. Sci. Paris 296, 881 (1983); S. Havlin, D. Ben‐Avraham, and H. Sompolinsky, Phys. Rev. A 27, 1730 (1983).en_US
dc.identifier.citedreferenceEquation (4) is the correct scaling relation for SN∣SN∣ however, in paper I, due to a typographical error the equation was given as SN(t→∞,p) = td2f[(ppc−1)t−(2ν−β+μ)].en_US
dc.identifier.citedreferenceD. W. Heermann and D. Stauffer, Z. Phys. B 44, 339 (1981); R. B. Pandey and D. Stauffer, J. Phys. A 16, L511 (1983); J. Adler, Z. Phys. B 55, 227 (1984); D. S. Gaunt and M. G. Sykes, J. Phys. A 16, 783 (1983).en_US
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dc.identifier.citedreferenceJ. S. Newhouse, Ph.D. thesis. University of Michigan, Ann Arbor, 1985.en_US
dc.owningcollnamePhysics, Department of


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